BTN is 18/0/1 over 12 hands. Basically no reads in a limped pot.

What's best on the river? b/f? c/f? c/c?

Full Tilt No-Limit Hold'em, $0.25 BB (6 handed) - Full Tilt Converter Tool from FlopTurnRiver.com

BB ($29.75)
UTG ($56.35)
Hero (MP) ($56.77)
CO ($47.40)
Button ($32.50)
SB ($24.75)

Preflop: Hero is MP with 2, 2
UTG calls $0.25, Hero calls $0.25, 1 fold, Button calls $0.25, 1 fold, BB checks

Flop: ($1.10) 2, Q, 3 (4 players)
BB checks, UTG checks, Hero bets $1, Button calls $1, BB calls $1, 1 fold

Turn: ($4.10) 5 (3 players)
BB checks, Hero bets $3.25, Button calls $3.25, BB calls $3.25

River: ($13.85) 9 (3 players)
BB checks, Hero checks, Button bets $5, 1 fold, Hero ?